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Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
Publisher: Cengage Learning
ISBN: 9781285195728

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BuyFindarrow_forward

Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
Publisher: Cengage Learning
ISBN: 9781285195728
Chapter A, Problem 12PE
Textbook Problem
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For Problems 7-20, expand and simplify.

( 2 x y ) 6

To determine

To expand:

(2xy)6.

Explanation of Solution

Let y=y.

The binomial expansion for (x+y)n is

xn+nxn1y+n(n1)2!.xn2y2+n(n1)(n2)3!xn3y3+........+yn

The exponents of x begin with the exponent of 6 and decrease term by term by 1 until the last term becomes 1, i.e. the exponent of x is 0.

The exponents of y begin with 0 and increase term by term by 1 until the last term contains the power of 6.

Therefore,

(2xy)6=(2x)6+6(2x)5(y)+652!(2x)4(y)2+6543!(2x)3(y)3+65434!(2x)2(y)4+654325!(2x)(y)5+(y)6

Here,

2!=213!=3214!=43215!=543&#

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